AN INTRODUCTION TO MATHEMATICAL COSMOLOGY Second Edition

Author: J. N. ISLAM

Published in: Cambridge University press

ISBN: 0-511-01849-5

File Type: pdf

File Size:  3 MB

Language: English



Description

The material in the earlier edition, to which there appears to have been a favorable response, has been kept intact as far as possible in this new edition except for minor changes. A number of new additions have been made. Some standard topics have been added to the introduction to general relativity, such as Killing vectors. Not all these topics are used later in the book, but some may be of use to the beginning student for mathematical aspects of cosmological studies. Observational aspects have been brought up to date in an extended chapter on the cosmological constant.

As this is a book on mathematical cosmology, the treatment of observations is not definitive or exhaustive by any means, but hopefully it is adequate. To clarify the role of the cosmological constant, much discussed inrecent years, an exact, somewhat unusual solution with cosmological constant is included. Whether the solution is new is not clear: it is meant toprovide a ‘comprehension exercise’. One reviewer of the earlier edition wondered why the Hubble constant and the deceleration parameter were chosen for a separate chapter. I believe these two parameters are among the most important in cosmology; adequate understanding of these helps to assess observations generally. Within the last year or two, through analyses of supernovae in distant galaxies, evidence seems to be emerging that the universe may be accelerating, or at least the deceleration may be not as much as was supposed earlier. If indeed the universe is accelerating, the nomenclature ‘deceleration parameter’ may be called into question. In any case, much more work has to be done, both observational and theoretical, to clarify the situation and it is probably better to retain the term, and refer to a possible acceleration as due to a ‘negative deceleration parameter’ (in case one has to revert back to ‘deceleration’!). I believe it makes sense, in most if not all subjects, constantly to refer back to earlier work, observational, experimental or practical, as well as theoretical aspects, for this helps to point to new directions and to assess new developments.

Some of the material retained from the first edition could be viewed in this way. A new exact inflationary solution for a sixth degree potential has been added to the chapter on the very early universe. The chapter on quantum cosmology is extended to include a discussion on functional differential equations, material which is not readily available. This topic is relevant for an understanding of the Wheeler–De Witt equation. Some additional topics and comments are considered in the Appendix at the end of the book. Needless to say, in the limited size and scope of the book an exhaustive treatment of any topic is not possible, but we hope enough ground has been covered for the serious student of cosmology to benefit from it.

As this book was going to press, Fred Hoyle passed away. Notwithstanding the controversies he was involved in, I believe Hoyle was one of the greatest contributors to cosmology in the twentieth century. The controversies, more often than not, led to important advances. Hoyle’s prediction of a certain energy level of the carbon nucleus, revealed through his studies of nucleosynthesis, confirmed later in the laboratory, was an out standing scientific achievement. A significant part of my knowledge of cosmology, for what it is worth, was acquired through my association with the then Institute of Theoretical Astronomy at Cambridge, of which the Founder-Director was Hoyle, who was kind enough to give me an appointment for some years. I shall always remember this with gratitude.

I am grateful to Clare Hall, Cambridge, for providing facilities where the manuscript and proofs were completed. I am grateful for helpful comments by various CUP readers and referees, although it has not been possible to incorporate all their suggestions. I thank the various reviewers of the earlier edition for useful comments. I am grateful to Simon Mitton, Rufus Neal, Adam Black and Tamsin van Essen for cooperation and help at various stages in the preparation of this edition. I thank ‘the three women in my life’ (Suraiya, Sadaf and Nargis) and my son-in-law Kamel for support and encouragement.
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